**IN THE ADJOINING FIGURE , TRIANGLE ABC IS AN ISOSCELES TRIANGLE IN WHICH AB=AC.IF E AND **

**F****BE THE MIDPOINTS OF**

**AC****AND**

__AB__RESPECTIVELY, **PROVE THAT BE=CF. **

**Given: **In ΔABC, AB = AC

and D and E are mid point of AB and AC

⇒ AD = BD = AE = CE .....(1)

In ΔABC

∠ABC = ∠ACB (Angles opposite to equal sides)

⇒ ∠DBC = ∠ECD ......(2)

Now, In ΔDBC and ΔECB

DB = EC (From (1))

∠DBC = ∠ECD (From (2))

BC = CB (Common)

So, ΔDBC ΔECB (By SAS congruency criterion)

⇒ BE = CF (CPCT)

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